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Theorem com3l 75
Description: Commutation of antecedents. Rotate left. (Contributed by NM, 25-Apr-1994.) (Proof shortened by Wolf Lammen, 28-Jul-2012.)
Hypothesis
Ref Expression
com3.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
Assertion
Ref Expression
com3l  |-  ( ps 
->  ( ch  ->  ( ph  ->  th ) ) )

Proof of Theorem com3l
StepHypRef Expression
1 com3.1 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
21com3r 73 . 2  |-  ( ch 
->  ( ph  ->  ( ps  ->  th ) ) )
32com3r 73 1  |-  ( ps 
->  ( ch  ->  ( ph  ->  th ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  com4l  78  impd  242  expdcom  1331  nebidc  2285  prel12  3542  reusv3  4192  relcoi1  4849  oprabid  5537  poxp  5853  reldmtpos  5868  tfrlem9  5935  tfri3  5953  ordiso2  6357  distrlem5prl  6684  distrlem5pru  6685  bndndx  8180  uzind2  8350  leexp1a  9309  bj-inf2vnlem2  10096
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